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- ItemAnalysis and Quantum Theory(Zürich : EMS Publ. House, 2005) Derezinski, Jan; Solovej, Jan-PhilipThe MFO-Workshop 0538 Analysis and Quantum Theory focussed on problems in mathematical physics, especially those connected to quantum field theory. Several theoretical physicists introduced a mostly mathematically oriented audience to topics in theoretical physics such as perturbative quantum field theory and fractional quantum Hall effect, thus bridging the gap between theoretical physics and mathematics. Apart from these reviews, a selection of research reports on recent results in mathematical physics was presented.
- ItemAlgebraic K-Theory(Zürich : EMS Publ. House, 2006) Huber-Klawitter, Annette; Jannsen, Uwe; Levine, MarcThis is the report on the Oberwolfach workshop Algebraic KTheory, held in July 2006. The talks covered mainly topics from Algebraic Geometry and Number Theory in connection with K-Theory. Special emphasis was placed on motivic cohomology and motivic homotopy of general schemes.
- ItemMini-Workshop: Statistical Methods for Inverse Problems(Zürich : EMS Publ. House, 2006) Reiß, MarkusInverse problems appear naturally in a broad range of applications. Numerical analysis and statistics have – often independently – developed methods for regularisation and inversion. The aim of this mini-workshop is to bring together these methods and to consider their use in applications, with a focus on mathematical finance.
- ItemAnalysis and Topology in Interaction(Zürich : EMS Publ. House, 2006) Goette, Sebastian; Igusa, Kiyoshi; Schick, ThomasThis workshop brought together, on the one side, mathematicians working in areas of global analysis and index theory, which are related with problems in algebraic topology, and on the other side, specialists in fields like surgery theory, higher homotopy theory or twisted cohomology theories. Its particular aim was to promote the flow of ideas and techniques between these two areas.
- ItemAnalysis and Geometric Singularities(Zürich : EMS Publ. House, 2005) Mazzeo, Rafe; Piazza, PaoloThis workshop focused on several of the main areas of current research concerning analysis on singular and noncompact spaces. Topics included harmonic analysis and Hodge theory on, and the theory of compactifications of, locally symmetric spaces, new topological techniques in index theory, nonlinear elliptic problems related to metrics with special geometry, and various more traditional problems in spectral geometry concerning estimation of eigenvalues and the spectral function.
- ItemMini-Workshop: Feinstrukturtheorie und Innere Modelle(Zürich : EMS Publ. House, 2006) Magidor, Menachem; Schindler, RalfThe main aim of fine structure theory and inner model theory can be summarized as the construction of models which have a canonical inner structure (a fine structure), making it possible to analyze them in great detail, and which at the same time reflect important aspects of the surrounding mathematical universe, in that they satisfy certain strong axioms of infinity, or contain complicated sets of reals. Applications range from obtaining lower bounds on the consistency strength of all sorts of set theoretic principles in terms of large cardinals, to proving the consistency of certain combinatorial properties, their compatibility with strong axioms of infinity, or outright proving results in descriptive set theory (for which no proofs avoiding fine structure and inner models are in sight). Fine structure theory and inner model theory has become a sophisticated and powerful apparatus which yields results that are among the deepest in set theory.
- ItemMini-Workshop: Convergence of Adaptive Algorithms(Zürich : EMS Publ. House, 2005) Carstensen, Carsten; Dörfler, WillyAdaptive refinement strategies are a key concept for the efficient numerical solution of partial differential equations. New findings allow the study of convergence and optimality of adaptive finite element methods. It was the aim of the Oberwolfach to discuss necessary conditions for optimal convergence and to extend the theory to new areas of application.
- ItemMini-Workshop: Dynamics of Cocycles and One-Dimensional Spectral Theory(Zürich : EMS Publ. House, 2005) Johnson, Russell; Lenz, DanielMany spectral questions about one-dimensional Schrödinger operators with quasi-periodic potentials can be reduced to dynamical questions about certain quasi-periodic SL(2, R)-valued cocycles. This connection has recently been employed to prove a number of long-standing conjectures. The aim of this mini-workshop was to bring together people from both spectral theory and dynamical systems in order to further develop and exploit the dynamical approach to quasi-periodic Schrödinger operators.
- ItemMini-Workshop: Analysis and Computation of Microstructures in Finite Plasticity(Zürich : EMS Publ. House, 2005) Conti, Sergio; Ortiz, MichaelPlastic material behaviour is typically the result of the interaction of complex substructures on a microscopic scale. Common models of finite plasticity are based on macroscopic, phenomenological approaches and do not take into account any microstructural information. The miniworkshop focuses on the application of methods from the calculus of variations to models for microstructures in plasticity. In particular, the investigation of the relaxation of the underlying functional, corresponding to quasiconvexification of the energy density, allows us to gain interesting microscopic as well as macroscopic information.
- ItemMini-Workshop: Anisotropic Motion Laws(Zürich : EMS Publ. House, 2006) Smereka, Peter; Voigt, AxelAnisotropic motion laws play a key role in many applications ranging from materials science, biophysics to image processing. All these highly diversified disciplines have made it necessary to develop common mathematical foundations and framworks to deal with anisotropy in geometric motion. The workshop brings together leading experts from various fields to address well-posedness, accuracy, and computational efficiency of the mathematical models and algorithms.